Skip to main content
SpringerLink
Log in

Development of a Predictive Equation for Modelling the Infiltration Process Using Gene Expression Programming

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

In this study, the soft computing technique of Gene expression programming (GEP) has been employed to generate a predictive equation of infiltration rate (fp). Infiltration experiments were conducted at 124 different sites and soil samples were collected to assess various soil properties throughout the Himalayan lake catchment. Parameters determined from observed data using nonlinear-Levenberg Marquardt algorithm were substituted in Horton, Kostiakov and Philip infiltration models and fp were predicted. Using soil data generated by laboratory investigation of soil samples, the GEP model was developed. Training and testing of the GEP model was performed using 70% and 30% of data respectively. Performance of GEP developed functional relationship was evaluated by comparing predictions from it and aforementioned infiltration models with field observed fp, and by applying overall performance index (OPI) computed using Coefficient of Determination (R2), Nash–Sutcliffe Efficiency (ENS), Willmott’s Index of Agreement (W), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Expression developed using GEP indicated feasibility of developed equation with ENS, R2, W, RMSE and MAE of 0.84, 0.84, 0.96, 1.9, and 0.8, respectively for training data-set and 0.84, 0.85, 0.95, 1.2, and 0.95, respectively for testing data-set. Comparative analysis revealed that though with a slightly higher OPI value (0.7–0.8), the performance of conventional models is better compared to the GEP model (0.66) but the GEP model having satisfactory performance may be used for fp prediction particularly in absence of observed data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig.1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability

The data being part of PhD research work can’t be shared at this stage but will be available upon request to the corresponding author.

References

  • Ali S, Islam A, Mishra PK, Sikka AK (2016) Green-Ampt approximations: A comprehensive analysis. J Hydrol 535:340–355. https://doi.org/10.1016/j.jhydrol.2016.01.065

    Article  Google Scholar 

  • Azamathulla HM, Ghani AA, Leow CS et al (2011) Gene-expression programming for the development of a stage-discharge curve of the Pahang River. Water Resour Manag 25(11):2901–2916. https://doi.org/10.1007/s11269-011-9845-7

    Article  Google Scholar 

  • Badar B, Romshoo SA, Khan MA (2013) Integrating biophysical and socioeconomic information for prioritizing watersheds in a Kashmir Himalayan lake: a remote sensing and GIS approach. Environ Monit Assess 185(8):6419–6445

  • Blacke GR, Hartge KH (1986) Bulk density in Klute A (ed) Methods of Soil Analysis, Part 1: Physical and Mineralogical Methods, Soil Science Society of America, Madison, WI, pp 363–375

  • Dashtaki SG, Homaee M, Mahdian MH, Kouchakzadeh M (2009) Site-dependence performance of infiltration models. Water Resour Manag 23(13):2777–2790

    Article  Google Scholar 

  • Deep K, Das KN (2008) Optimization of infiltration parameters in hydrology. World Journal of Modelling and Simulation 4:120–130

    Google Scholar 

  • Duan R, Fedler CB, Borrelli J (2011) Field evaluation of infiltration models in lawn soils. Irrigation Sci 29:379–389. https://doi.org/10.1007/s00271-010-0248-y

    Article  Google Scholar 

  • Ferreira C (2001a) Gene expression programming in problem solving. In: 6th Online World Conference on Soft Computing in Industrial Applications (Invited Tutorial)

  • Ferreira C (2001b) Gene expression programming: a new adaptive algorithm for solving problems. Complex System 13:87–129

    Google Scholar 

  • Ferreira C (2002) Gene Expression Programming in Problem Solving. In: Roy R, Köppen M, Ovaska S, Furuhashi T, Hoffmann F (ed) Soft Computing and Industry. Springer, London

  • Gee GW, Bauder JW (1986) Particle-size analysis in Klute A (ed) Methods of soil analysis, Part1: Physical and Mineralogical Method, Soil Science Society of America, Madison, WI, pp 383–412

  • Green WH, Ampt GA (1911) Studies on Soil Physics. J Agric Sci 4:1–24. https://doi.org/10.1017/S0021859600001441

    Article  Google Scholar 

  • Guven A, Aytek A, Yuce MI, Aksoy H (2008) Genetic programming based empirical model for daily reference evapotranspiration estimation. Clean-Soil Air Water 36(10–11):905–912

    Article  Google Scholar 

  • Guven A, Aytek A (2009) New approach for stage–discharge relationship: gene-expression programming. J Hydrolog Eng 14(8):812–820

    Article  Google Scholar 

  • Guven A, Kisi Ö (2010) Daily pan evaporation modeling using linear genetic programming technique. Irrigat Sci 29(2):135–145

    Article  Google Scholar 

  • Guven A, Kisi Ö (2011) Estimation of suspended sediment yield in natural rivers using machine-coded linear genetic programming. Water Resour Manag 25:691–704

    Article  Google Scholar 

  • Holtan HN (1961) Concept for infiltration estimates in watershed engineering ARS 41–51. U S Department of Agriculture, Agricultural research service, Washington, DC

    Google Scholar 

  • Horton RE (1941) An approach toward a physical interpretation of infiltration-capacity 1. Soil Sci Soc Am J 5:399–417. https://doi.org/10.2136/sssaj1941.036159950005000C0075x

    Article  Google Scholar 

  • Kale RV, Sahoo B (2011) Green-Ampt infiltration models for varied field conditions: A revisit. Water Resour Manag 25(14): 3505–3536. https://doi.org/10.1007/s11269-011-9868-0

  • Kostiakov AN (1932) On the dynamics of the coefficient of water-percolation in soils and on the necessity for studying it from a dynamic point of view for purposes of amelioration. Society of Soil Science 14:17–21

    Google Scholar 

  • Kalogirou SA (2001) Artificial neural networks in the renewable energy systems applications: a review. Renew Sustain Energy Rev 5:373–401

    Article  Google Scholar 

  • Khan M, Azamathulla H M, Tufail, M, Ab Ghani A (2012) Bridge pier scour prediction by gene expression programming. In Proceedings of the Institution of Civil Engineers-Water Management 165(9):481–493. https://doi.org/10.1680/wama.11.00008

  • Legates DR, McCabe GJ (1999) Evaluating the use of ‘‘goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241

    Article  Google Scholar 

  • Ma D, Shao M (2008) Simulating infiltration into stony soils with a dual-porosity model. Eur J of Soil Sci 59:950–959

    Article  Google Scholar 

  • Machiwal D, Jha MK, Mal BC (2006) Modelling infiltration and quantifying spatial soil variability in a wasteland of Kharagpur, India. Biosyst Eng 95:569–582. https://doi.org/10.1016/j.biosystemseng.2006.08.007

    Article  Google Scholar 

  • Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind App Math 11:431–441. https://doi.org/10.1137/0111030

    Article  Google Scholar 

  • Mazloom H, Foladmand H (2013) Evaluation and determination of the coefficients of infiltration models in Marvdasht region, Fars province. Int J Adv Biol Biomed Res 1:822–829

    Google Scholar 

  • Mishra SK, Tyagi JV, Singh VP (2003) Comparison of infiltration models Hydrol Processs 17:2629–2652. https://doi.org/10.1002/hyp.1257

    Article  Google Scholar 

  • Mirzaee S, Zolfaghari AA, Gorji M, Dyck M, Dashtaki SG (2013) Evaluation of infiltration models with different numbers of fitting parameters in different soil texture classes. Arch Agron Soil Sci 60(5):1–13. https://doi.org/10.1080/03650340.2013.823477

  • Moriasi DN, Arnold JG, Van Liew MW, Bingner RL et al (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900

    Article  Google Scholar 

  • Muzzammil M, Alama J, Danish M (2015) Scour prediction at bridge piers in cohesive bed using gene expression programming. Aquat Procedia 4:789–796. https://doi.org/10.1016/j.aqpro.2015.02.098

    Article  Google Scholar 

  • Oyedele O, Akpa EA, Akpan JF (2019) Evaluation of Infiltration Characteristics of Soils Developed on Coastal Plain Sands in Calabar Municipality Local Government Area, Cross River State, Nigeria’. Asian Journal of Advances in Agricultural Research 10:1–8. https://doi.org/10.9734/ajaar/2019/v10i430036

    Article  Google Scholar 

  • Parhi PK, Mishra SK, Singh R (2007) A modification to Kostiakov and Modified Kostiakov infiltration models. Water Resour Manag 21:1973–1989

    Article  Google Scholar 

  • Philip JR (1957) The theory of infiltration: 1 the infiltration equation and its solution. Soil Sci 83: 345–357. https://doi.org/10.1097/00010694-200606001-00009

  • Rao MD, Raghuwanshi NS, Singh R (2006) Development of a physically based 1D-infiltration model for seal formed irrigated soils. Agric Water Manage 84(1–2):164–174

    Google Scholar 

  • Rasool T, Dar AQ, Wani MA (2020) Comparison of infiltration model parameter estimation techniques under different land use/land covers International journal of Hydrology sciences and Technology (in press)

  • Richard LA (1931) Capillary conduction of liquids through porous mediums. Physics 1:318–333. https://doi.org/10.1063/1.1745010

    Article  Google Scholar 

  • Saxton KE, Willey PH (2006) The SPAW model for agricultural field and pond hydrologic simulation. Watershed models, 401–435

  • Shao Q, Baumgartl T (2014) Estimating input parameters for four infiltration models from basic soil, vegetation, and rainfall properties. Soil Sci Soc Am J 78:1507–1521. https://doi.org/10.2136/sssaj2014.04.0122

    Article  Google Scholar 

  • Skaggs RW, Khaleel R (1982) Chapter 4: Infiltration. In Haan CT (ed) Hydrologic Modeling of Small Watersheds. Am Soc Agric Eng pp 119–166

  • Smith RE (1972) The infiltration envelope: results from a theoretical infiltrometer. J Hydrol 17:1–22. https://doi.org/10.1016/0022-1694(72)90063-7

    Article  Google Scholar 

  • Smith RE, Parlange JY (1978) A parameter-efficient hydrologic infiltration model. Water Resour Res 14:533–538. https://doi.org/10.1029/WR014i003p00533

    Article  Google Scholar 

  • Soil Survey Division Staff (1993) Soil survey manual. Soil Conservation Service. United States Department of Agriculture Handbook, vol. 18. USDA, Washington, DC

  • Seyedzadeh A, Panahi A, Maroufpoor E (2020) A new analytical method for derivation of infiltration parameters. Irrig Sci 38:449–460

    Article  Google Scholar 

  • Sihag P, Singh B, Sepah Vand A, Mehdipour V (2018) Modeling the infiltration process with soft computing techniques. ISH J Hydraul Eng 26(2):138–152. https://doi.org/10.1080/09715010.2018.1464408

  • SPSS (2011) Statistical package for social sciences. Release 20.0. SPSS Inc, Chicago Il

  • Tabbussum R, Dar AQ (2021) Performance evaluation of artificial intelligence paradigms—artificial neural networks, fuzzy logic, and adaptive neuro-fuzzy inference system for flood prediction. Environ Sci Pollut Res 1-18. https://doi.org/10.1007/s11356-021-12410-1

  • Traore S, Guven A (2012) Regional-specific numerical models of evapotranspiration using gene-expression programming interface in Sahel. Water Resour Manag 26(15):4367–4380

    Article  Google Scholar 

  • Traore S, Luo Y, Fipps G (2017) Gene-expression programming for short-term forecasting of daily reference evapotranspiration using public weather forecast information. Water Resour Manag 31(15):4891–4908

    Article  Google Scholar 

  • Walkley A, Black IA (1934) An examination of the Degtjareff method for determining soil organic matter and a proposed modification of the chromic acid titration method. Soil Sci 37(1):29–38

    Article  Google Scholar 

  • Yassin MA, Alazba AA, Mattar MA (2016) A new predictive model for furrow irrigation infiltration using gene expression programming. Comput Electron Agric 122:168–175. https://doi.org/10.1016/j.compag.2016.01.035

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the Head of Department, Civil Engineering, National Institute of Technology Srinagar for providing adequate laboratory facilities.

Funding

The authors would like to thank the Ministry of Human Resources and Development, India for funding the research.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Srinagar, Hazratbal, Srinagar, Union Territory of Jammu and Kashmir, 190006, India

    Tabasum Rasool & A. Q. Dar

  2. Research and Extension, HMAARI, Leh, Ladakh, J&K, 194101, India

    M. A. Wani

Authors
  1. Tabasum Rasool
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Q. Dar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. Wani
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Tabasum Rasool designed the study, obtained the data and prepared it for simulation and statistical analysis, and wrote the first draft of manuscript, and is the guarantor. Author Abdul Qayoom Dar managed the literature searches. Author Mushtaq Ahmad Wani contributed to the preparation of the final manuscript.

Corresponding author

Correspondence to Tabasum Rasool.

Ethics declarations

Conflict of Interest/ Competing Interest

The authors declare that they do not have any conflict of interest to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rasool, T., Dar, A.Q. & Wani, M.A. Development of a Predictive Equation for Modelling the Infiltration Process Using Gene Expression Programming. Water Resour Manage 35, 1871–1888 (2021). https://doi.org/10.1007/s11269-021-02816-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-021-02816-4

Keywords

Search

Navigation